All Downhill from Here

What Automatic Differentiation can Do for Optics

Benjamin Pope, NYU

Slides available at
benjaminpope.github.io/talks/uqphysics/uqphysics.html

Work in collaboration with Sydney students Alison Wong (PhD)

and Louis Desdoigts (Honours)

and faculty Peter Tuthill (Sydney)/Laurent Pueyo (STScI).

See also our work \& DP on JWST Aperture Masking Interferometer - hiring a postdoc and PhD student!

Direct Imaging

We are starting to detect planets at the epoch of formation - eg the accreting protoplanets PDS 70 bc.

ESO/A. Müller et al.

(ESO/A. Müller et al.)

Candidate around our nearest neighbour, α Cen!

Wagner et al

(Wagner et al., 2021)

The main limitation on direct imaging is from wavefront aberrations which corrupt phase information.

Good and Bad PSFs

Coronagraphs

Lyot and his coronagraph

Lyot Coronagraph - Credit: Rebecca Oppenheimer, Lyot Project

Lyot Diagram

Credit: Rebecca Oppenheimer, Lyot Project

Emiel Por Coronagraph

Phase Apodized Coronagraph: Por, 2019, arXiv:1908.02585

Toliman Space Telescope

Book of Fixed Stars
Book of Fixed Stars,
'Abd al-Rahman al-Sufi,
MS. Marsh 144,
Bodleian Library
Book of Fixed Stars
rijl qanturis
which is the one drawn
on the southern astrolabe

Detect planets with μ-arcsec astrometry

Astrometric precision proportional to gradient energy

Use diffractive optic to maximize this subject to constraints

Toliman Pupil and Stars

Early pupil design & simulation

Toliman Mask

TOLIMAN lab test phase mask

Automatic Differentiation

So how do we design such complicated optical systems in a principled way?

What if we want to linearize an arbitrary optical system?

Optics is mathematically like machine learning: matrix multiplications and simple nonlinear functions

Can use automatic differentiation!

Autodiff is the enabling technology for deep neural networks - you use the chain rule to take derivatives of nearly-arbitrary numerical functions.

Implementations in TensorFlow, PyTorch, Julia native...

Here we use Google Jax, which resembles NumPy, to rewrite the Fourier/Fresnel optics code poppy to take derivatives

Morphine!

Comparable work in the DeepOptics group at Stanford

Louis Desdoigts - sensitivity of Toliman telescope design to Zernike modes

Toliman Image

Alison Wong - phase retrieval and design by gradient descent

Phase Retrieval

Phase Retrieval

Phase Retrieval with Saturation

Phase Retrieval with Saturation

Coronagraph Designs

Coronagraph Phase Mask Design

Continuous Latent-Image Mask Binarization (CLIMB)

Basis

Basis used in CLIMB

Toliman Designs

Toliman Phase Mask Designs

Kernel Phase

In radio astronomy the idea of 'closure phase' was developed to be immune to phase noise:

Correlate baselines around a triangle of receivers

JWST has an aperture masking instrument on NIRISS to obtain closure phases

JWST Aperture Mask
Kernel phase is a generalization of closure phase to arbitrary pupils.

Linearize response to phase noise: suitable for stable high Strehl images, with point-source calibrators

Separate out linear subspaces of Fourier components that are immune to phase noise vs susceptible

Used this in Pope et al, 2013 to revisit the Reid et al 2006, 2008 HST NICMOS volume-limited brown dwarf surveys and discover 5 additional tight binaries.
The other subspace can be used for wavefront sensing

Every point source image gives you a free wavefront measurement in the instrument pupil!

Cophasing segmented mirror in the lab (Pope+2014)

Cophasing

Jacobian of Palomar PHARO camera wrt phase

Pharo Jacobian
Extending kernel phase to coronagraphy has the same feature of a noise-corrupted space and a kernel space Singular values

The Future

Get using morphine and read the paper!

What else can we use this for?

Spatial light modulator enabled technology!

Particle beams?

Questions!